Cambridge IGCSE Mathematics - International 0607 — 2020 May/June Paper 2 · Variant 3

1 (a) Write 0.047 996 correct to 4 decimal places. ...................................................... [1] (b) Write 60 449 correct to 3 significant figures. ...................................................... [1]

Mark scheme: Question Answer Marks Partial Marks 1(a) 0.0480 1 1(b) 60 400 1

More questions on Estimation

2 Work out 4 - 1 . 4 6 Give your answer as a mixed number in its simplest form. .................................................... [3]

Mark scheme: 2 5 3 B2 for equivalent mixed number or improper fraction 212 3 10 or B1 for 4 − 1 oe 12 12 51 22 or − oe 12 12

More questions on Fractions, decimals and percentages

3 Simplify. a 2 # a 5 a 3 .................................................... [2]

Mark scheme: 3 a4 2 B1 for a7 or a–1 × a5 or a2 × a2

More questions on Indices I

4 (a) Write down the mathematical name of the quadrilateral that has rotational symmetry of order 2 but no lines of symmetry. .................................................... [1] (b) Write down the mathematical name of the quadrilateral that has exactly one line of symmetry. .................................................... [1]

Mark scheme: 4(a) Parallelogram 1 4(b) Kite or Isosceles Trapezium 1

More questions on Symmetry

5 Solve. 9 - 2x G 5 (x + 6) .................................................... [3]

Mark scheme: 5 x ⩾ –3 3 B2 for x * –3 where * is = or < or > or ⩽ or M1 for 9 – 2x ⩽ 5x + 30 M1FT for correctly isolating terms

More questions on Inequalities

6 A biased four-sided spinner is spun 150 times. The number of times that the spinner lands on each number is shown in the table. Number on spinner 1 2 3 4 Frequency 34 63 27 26 (a) Write down the relative frequency of the spinner landing on 2. .................................................... [1] (b) Explain why it is reasonable to use your answer to part (a) as the probability of this spinner landing on 2. ............................................................................................................................................................ [1] (c) The spinner is spun 3000 times. Find the expected number of times that the spinner lands on 2. .................................................... [2]

Mark scheme: 6(a) 63 1 oe 150 6(b) Large sample oe 1 6(c) 1260 2 63 M1 for their × 3000 oe 150

More questions on Relative and expected frequencies

7 Divide 96 cm in the ratio 5 : 3. ............................ cm , ....................... cm [2]

Mark scheme: 7 60, 36 2 B1 for each or M1 for 96 ÷ (5 + 3)

More questions on Ratio and proportion

8 A is the point (- 2, 4 ) and B is the point (7, 1 ) . Find the length of AB giving your answer in its simplest surd form. ...................................................... [4]

Mark scheme: 8 3 10 4 B3 for 90 or B1 for 9 and 3 seen M1 for (their 9)2 + (their 3)2

More questions on Length and midpoint

9 P B Q 56° A 98° NOT TO SCALE C 57° D A, B, C and D are points on the circle. PBQ is a straight line. (a) Find angle DCB, giving a reason for your answer. Angle DCB = ................................... because .......................................................................................... ............................................................................................................................................................ [2] (b) Is PBQ a tangent to the circle? Give a reason for your answer. ................................... because ................................................................................................................. ............................................................................................................................................................ [1]

Mark scheme: 9(a) 82 2 B1 for each Opposite angles of a cyclic quadrilateral [add up to 180] oe 9(b) No and any mention of Alternate 1 Segment Theorem oe

More questions on Circle theorems I

10 Solve the simultaneous equations. 2x + 3y = 5 y = 3x + 9 x = .................................................... y = .................................................... [3]

Mark scheme: 10 x = –2, y = 3 3 M1 for correct equation in x or equalising coefficients of x or y and adding / subtracting appropriately. B1 for one correct solution If 0 scored, SC1 for a correct substitution and evaluation of the other variable

More questions on Equations

11 The table shows some trigonometric ratios, each correct to 3 decimal places. Sine Cosine Tangent 40° 0.643 0.766 0.839 70° 0.940 0.342 2.747 Use this information to find (a) sin110°, .................................................... [1] (b) tan320°. .................................................... [1]

Mark scheme: 11(a) 0.940 1 11(b) –0.839 1

More questions on Trigonometric functions

12 Factorise completely. (a) 4x 2 y - 6xy 2 .................................................... [2] (b) 9x 2 - 1 .................................................... [1]

Mark scheme: 12(a) 2xy(2x – 3y) 2 B1 for any correct partially factorised expression 12(b) (3x + 1)(3x – 1) 1

More questions on Algebraic manipulation

13 Solve. (a) log x 9 = 2 x = .................................................... [1] (b) 2 log x - log 4 = log 9 x = .................................................... [2]

Mark scheme: 13(a) 3 1 13(b) 6 2 M1 for any correct use of  a  loga – log b = log   or  b  loga + log b = log (a × b) or nloga = logan

More questions on The logarithmic function

14 y varies inversely as the square root of x. When x = 25 , y = 6 . Find y in terms of x. y = ..................................................... [2] Question 15 is printed on the next page.

Mark scheme: 14 30 2 k y = M1 for y = oe x x

More questions on Proportion

15 (a) On the Venn Diagram, shade the set A + B + C l. U B A C [1] (b) Use set notation to describe the shaded region. U Q P R .................................................... [1]

Mark scheme: 15(a) 1 15(b) ′ 1 ( P ∪ Q ) ∩ R

More questions on Sets